الْبَادِي بِالسَّلَامِ بَرِيءٌ مِنَ الْكِبْرِ
Meaning: One who starts the greeting is free from arrogance.
الْبَادِي is the person being described (mubtadaʾ). It conveys “the one who begins,” a form indicating the doer of an action. بَرِيءٌ is the predicate (khabar) describing that person.
بِالسَّلَامِ explains the act in which they take the initiative; مِنَ الْكِبْرِ explains what they are free from. The two prepositions carry different meanings: بِـ (“with/in”) and مِنْ (“from”).